Swift displaying the time or date based on timestamp

I have an API that returns data including a timestamp for that record.
In swift I have the timestamp element loaded and converted into a double and can then convert that into time. I want to be able to return the time if the date of the record is today and return the date if the record is not today.
See below:

let unixTimeString:Double = Double(rowData["Timestamp"] as! String)!
let date = NSDate(timeIntervalSince1970: unixTimeString) // This is on EST time and has not yet been localised.
var dateFormatter = NSDateFormatter()
dateFormatter.timeStyle = .ShortStyle
dateFormatter.doesRelativeDateFormatting = true
// If the date is today then just display the time, if the date is not today display the date and change the text color to grey.
var stringTimestampResponse = dateFormatter.stringFromDate(date)
cell.timestampLabel.text = String(stringTimestampResponse)

Do I use NSCalendar to see if 'date' is today and then do something?
How do you then localise the time so that its correct for the user rather than server time?